{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d6b0f8b0",
   "metadata": {},
   "source": [
    "| [03_data_science/05_SciPy统计分布.ipynb](https://github.com/shibing624/python-tutorial/blob/master/03_data_science/05_SciPy统计分布.ipynb)  | Scipy统计分布  |[Open In Colab](https://colab.research.google.com/github/shibing624/python-tutorial/blob/master/03_data_science/05_SciPy统计分布.ipynb) |\n",
    "\n",
    "# SciPy统计分布\n",
    "\n",
    "## SciPy的简介\n",
    "\n",
    "SciPy是建立在在Numpy基础上的科学计算库，提供大量的科学计算支持。\n",
    "\n",
    "在科学计算中我们往往会用到如下4个常用而又强大的功能：\n",
    "\n",
    "*    数值优化：scipy.optimize, 最优问题的数值近似解问题能够得到求解\n",
    "*    数值积分：scipy.integrate, 能够从数值角度求解积分问题，可以当作解析解的验证手段；同时也能够像Matlab一样求解微分方程\n",
    "*    插值算法：scipy.interpolate, 采样精度过低时可以使用interpolate得到连续曲线\n",
    "*    信号处理：scipy.signal, scipy.fftpack 滤波器和时间序列模型在数学上有异曲同工之妙，此处用这些库实现信号处理功能\n",
    "\n",
    "SciPy的其他重要内容会在其他内容中反复提及，比如\n",
    "\n",
    "*    线性代数：scipy.linalg直接映射了np.linalg的功能，如矩阵特征值分解、SVD分解、QR分解等。\n",
    "*    统计功能：scipy.stats具有强大的统计分布生成、探索、检查功能，在统计分布/随机数生成部分中结合理论介绍。\n",
    "*    稀疏矩阵：scipy.sparse在NumPy基础和NetworkX部分有所提及，在网络图模型中占有一席之地。\n",
    "*    科学函数：scipy.special, 能够快速给出一些科学函数的值（常见的如贝塞尔函数，排列组合数等）\n",
    "\n",
    "### 子模块\n",
    "\n",
    "|子模块|描述|\n",
    "|:----|:----|\n",
    "|cluster|聚类算法|\n",
    "|constants|物理数学常数|\n",
    "|fftpack|快速傅里叶变换|\n",
    "|integrate|积分和常微分方程求解|\n",
    "|interpolate|插值|\n",
    "|io|输入输出|\n",
    "|linalg|线性代数|\n",
    "|odr|正交距离回归|\n",
    "|optimize|优化和求根|\n",
    "|signal|信号处理|\n",
    "|sparse|稀疏矩阵|\n",
    "|spatial|空间数据结构和算法|\n",
    "|special|特殊方程|\n",
    "|stats|统计分布和函数|\n",
    "|weave|调用C/C++|\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57fe4d3b",
   "metadata": {},
   "source": [
    "使用scipy之前，基础模块需要导入："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "d8fc5649",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9dadbf20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.        , -2.93939394, -2.87878788, -2.81818182, -2.75757576,\n",
       "       -2.6969697 , -2.63636364, -2.57575758, -2.51515152, -2.45454545,\n",
       "       -2.39393939, -2.33333333, -2.27272727, -2.21212121, -2.15151515,\n",
       "       -2.09090909, -2.03030303, -1.96969697, -1.90909091, -1.84848485,\n",
       "       -1.78787879, -1.72727273, -1.66666667, -1.60606061, -1.54545455,\n",
       "       -1.48484848, -1.42424242, -1.36363636, -1.3030303 , -1.24242424,\n",
       "       -1.18181818, -1.12121212, -1.06060606, -1.        , -0.93939394,\n",
       "       -0.87878788, -0.81818182, -0.75757576, -0.6969697 , -0.63636364,\n",
       "       -0.57575758, -0.51515152, -0.45454545, -0.39393939, -0.33333333,\n",
       "       -0.27272727, -0.21212121, -0.15151515, -0.09090909, -0.03030303,\n",
       "        0.03030303,  0.09090909,  0.15151515,  0.21212121,  0.27272727,\n",
       "        0.33333333,  0.39393939,  0.45454545,  0.51515152,  0.57575758,\n",
       "        0.63636364,  0.6969697 ,  0.75757576,  0.81818182,  0.87878788,\n",
       "        0.93939394,  1.        ,  1.06060606,  1.12121212,  1.18181818,\n",
       "        1.24242424,  1.3030303 ,  1.36363636,  1.42424242,  1.48484848,\n",
       "        1.54545455,  1.60606061,  1.66666667,  1.72727273,  1.78787879,\n",
       "        1.84848485,  1.90909091,  1.96969697,  2.03030303,  2.09090909,\n",
       "        2.15151515,  2.21212121,  2.27272727,  2.33333333,  2.39393939,\n",
       "        2.45454545,  2.51515152,  2.57575758,  2.63636364,  2.6969697 ,\n",
       "        2.75757576,  2.81818182,  2.87878788,  2.93939394,  3.        ])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 径向基函数\n",
    "x = np.linspace(-3, 3, 100)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "31ce26a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 高斯函数\n",
    "plt.plot(x, np.exp(-1 * x ** 2))\n",
    "plt.title(\"Gaussian\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "395d14fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.savefig('Gaussian.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2817458e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "os.path.exists('Gaussian.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f6235a5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 高维 RBF 插值\n",
    "# 三维数据点：\n",
    "x, y = np.mgrid[-np.pi / 2:np.pi / 2:5j, -np.pi / 2:np.pi / 2:5j]\n",
    "z = np.cos(np.sqrt(x ** 2 + y ** 2))\n",
    "fig = plt.figure(figsize=(12, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "ax.scatter(x, y, z)\n",
    "fig.savefig(\"mplot3d.jpg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "232b85f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "os.remove('Gaussian.png')\n",
    "os.remove('mplot3d.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81d35b9d",
   "metadata": {},
   "source": [
    "## 统计模块：stats\n",
    "\n",
    "Python 中常用的统计工具有 Numpy, Pandas, PyMC, StatsModels 等。\n",
    "Scipy 中的子库 scipy.stats 中包含很多统计上的方法。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cf4942a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean, 1.7559999999999998\n",
      "min, 1.46\n",
      "max 2.01\n",
      "stand deviation, 0.15081114017207078\n"
     ]
    }
   ],
   "source": [
    "# Numpy 自带简单的统计方法：\n",
    "heights = np.array([1.46, 1.79, 2.01, 1.75, 1.56, 1.69, 1.88, 1.76, 1.88, 1.78])\n",
    "print('mean,', heights.mean())\n",
    "print('min,', heights.min())\n",
    "print('max', heights.max())\n",
    "print('stand deviation,', heights.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06eedc75",
   "metadata": {},
   "source": [
    "导入 Scipy 的统计模块："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9f685935",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mode,  ModeResult(mode=array([1.88]), count=array([2]))\n",
      "skewness,  -0.3935244564726347\n",
      "kurtosis,  -0.33067209772439865\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats.stats as st\n",
    "\n",
    "print('mode, ', st.mode(heights))  # 众数及其出现次数\n",
    "print('skewness, ', st.skew(heights))  # 偏度\n",
    "print('kurtosis, ', st.kurtosis(heights))  # 峰度"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67b3762c",
   "metadata": {},
   "source": [
    "### 概率分布\n",
    "常见的连续概率分布有：\n",
    "- 均匀分布\n",
    "- 正态分布\n",
    "- 学生t分布\n",
    "- F分布\n",
    "- Gamma分布\n",
    "...\n",
    "- 离散概率分布：\n",
    "- 伯努利分布\n",
    "- 几何分布\n",
    "...\n",
    "\n",
    "这些都可以在 scipy.stats 中找到。\n",
    "\n",
    "它包含四类常用的函数：\n",
    "\n",
    "- norm.cdf 返回对应的累计分布函数值\n",
    "- norm.pdf 返回对应的概率密度函数值\n",
    "- norm.rvs 产生指定参数的随机变量\n",
    "- norm.fit 返回给定数据下，各参数的最大似然估计（MLE）值\n",
    "\n",
    " 从正态分布产生500个随机点：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "839225c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 正态分布\n",
    "from scipy.stats import norm\n",
    "x_norm = norm.rvs(size=500)\n",
    "x_norm.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e515858e",
   "metadata": {},
   "source": [
    "直方图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7c29fcb0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts,  [  7.  22.  44.  56.  75. 117.  76.  47.  40.  16.]\n",
      "bin centers [-2.61331997 -2.11619356 -1.61906715 -1.12194073 -0.62481432 -0.1276879\n",
      "  0.36943851  0.86656493  1.36369134  1.86081775  2.35794417]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ion() #开启interactive mode\n",
    "\n",
    "h = plt.hist(x_norm)\n",
    "print('counts, ', h[0])\n",
    "print('bin centers', h[1])\n",
    "figure = plt.figure(1)  # 创建图表1\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c989887",
   "metadata": {},
   "source": [
    "归一化直方图（用出现频率代替次数），将划分区间变为 20（默认 10）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "73c8c357",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = plt.hist(x_norm, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f376f528",
   "metadata": {},
   "source": [
    "在这组数据下，正态分布参数的最大似然估计值为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9ade45ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean,  0.04107482632105179\n",
      "x_std,  1.0107711572543323\n"
     ]
    }
   ],
   "source": [
    "x_mean, x_std = norm.fit(x_norm)\n",
    "\n",
    "print('mean, ', x_mean)\n",
    "print('x_std, ', x_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b8aef5a",
   "metadata": {},
   "source": [
    "将真实的概率密度函数与直方图进行比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d649640f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = plt.hist(x_norm, bins=20)\n",
    "\n",
    "x = np.linspace(-3, 3, 50)\n",
    "p = plt.plot(x, norm.pdf(x), 'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af9412db",
   "metadata": {},
   "source": [
    "积分函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d81ca889",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95.45% of the values lie between -2 and 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import trapz\n",
    "\n",
    "x1 = np.linspace(-2, 2, 108)\n",
    "p = trapz(norm.pdf(x1), x1)\n",
    "print('{:.2%} of the values lie between -2 and 2'.format(p))\n",
    "\n",
    "plt.fill_between(x1, norm.pdf(x1), color='red')\n",
    "plt.plot(x, norm.pdf(x), 'k-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4881049",
   "metadata": {},
   "source": [
    "可以通过 loc 和 scale 来调整这些参数，一种方法是调用相关函数时进行输入："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "26e1dd07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-3, 3, 50)\n",
    "p = plt.plot(x, norm.pdf(x, loc=0, scale=1))\n",
    "p = plt.plot(x, norm.pdf(x, loc=0.5, scale=2))\n",
    "p = plt.plot(x, norm.pdf(x, loc=-0.5, scale=.5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d3b9ec37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 不同参数的对数正态分布：\n",
    "from scipy.stats import lognorm\n",
    "\n",
    "x = np.linspace(0.01, 3, 100)\n",
    "\n",
    "plt.plot(x, lognorm.pdf(x, 1), label='s=1')\n",
    "plt.plot(x, lognorm.pdf(x, 2), label='s=2')\n",
    "plt.plot(x, lognorm.pdf(x, .1), label='s=0.1')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "024cd338",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 离散分布\n",
    "from scipy.stats import randint\n",
    "\n",
    "# 离散均匀分布的概率质量函数（PMF）：\n",
    "high = 10\n",
    "low = -10\n",
    "\n",
    "x = np.arange(low, high + 1, 0.5)\n",
    "p = plt.stem(x, randint(low, high).pmf(x))  # 杆状图\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2864edd8",
   "metadata": {},
   "source": [
    "### 假设检验\n",
    "相关的函数：\n",
    "\n",
    "1. 正态分布\n",
    "2. 独立双样本 t 检验，配对样本 t 检验，单样本 t 检验\n",
    "3. 学生 t 分布\n",
    "\n",
    "导入函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c4548251",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import ttest_ind\n",
    "\n",
    "# 独立样本 t 检验\n",
    "# 两组参数不同的正态分布：\n",
    "n1 = norm(loc=0.3, scale=1.0)\n",
    "n2 = norm(loc=0, scale=1.0)\n",
    "\n",
    "# 从分布中产生两组随机样本：\n",
    "n1_samples = n1.rvs(size=100)\n",
    "n2_samples = n2.rvs(size=100)\n",
    "\n",
    "# 将两组样本混合在一起：\n",
    "samples = np.hstack((n1_samples, n2_samples))\n",
    "\n",
    "# 最大似然参数估计：\n",
    "loc, scale = norm.fit(samples)\n",
    "n = norm(loc=loc, scale=scale)\n",
    "\n",
    "# 比较：\n",
    "x = np.linspace(-3, 3, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ba6fab09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([samples, n1_samples, n2_samples])\n",
    "plt.plot(x, n.pdf(x), 'b-')\n",
    "plt.plot(x, n1.pdf(x), 'g-')\n",
    "plt.plot(x, n2.pdf(x), 'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d50fd97e",
   "metadata": {},
   "source": [
    "独立双样本 t 检验的目的在于判断两组样本之间是否有显著差异："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0f9301d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = 4.238039942388443\n",
      "p-value = 3.4551178415131466e-05\n"
     ]
    }
   ],
   "source": [
    "t_val, p = ttest_ind(n1_samples, n2_samples)\n",
    "\n",
    "print('t = {}'.format(t_val))\n",
    "print('p-value = {}'.format(p))\n",
    "# t = 0.868384594123\n",
    "# p-value = 0.386235148899"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7d9369f",
   "metadata": {},
   "source": [
    "p 值小，说明这两个样本有显著性差异。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7624fb7",
   "metadata": {},
   "source": [
    "本节完。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "330b27cb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}